Stabilization of Ion-Temperature-Gradient–Driven Tokamak Modes by Magnetic-Field Gradient Reversal

Abstract

Global gyrokinetic particle simulations have been used to search tokamak configurations which are stable against the ion-temperature-gradient-driven (ITG) modes commonly held responsible for the core anomalous ion heat transport. The stable configurations are characterized by strongly reduced or reversed =B drifts on the low-field side. Since excellent transport properties have been observed in high b p (poloidal beta) tokamak experiments, we conjecture, as a result of our simulations, that this may be due to the stabilization of ITG modes by the reduction of the =B drifts.[S0031-9007 (97)03019-6] PACS numbers: 52.55.Fa, 52.35.Kt, 52.55.Dy, 52.65.TtIon-temperature-gradient-driven (ITG) instabilities are now commonly held responsible for the turbulence giving rise to anomalous ion heat transport in the core of tokamaks; ITG-based transport models have been claimed to predict successfully the plasma thermal transport over a wide range of parameters [1][2][3]. The reduction of this transport would be of great help in the achievement of a fusion reactor; configurations that are free of these instabilities are of very high interest. An effort has recently been made to find such configurations; e.g., oblate plasmas [4] and plasmas with sheared rotation (e.g., [2] and [5]) have been discussed as routes to ITG-mode stabilization. We propose here another route to ITG stability: the reduction of the =B drift on the low-field side of the torus.In this Letter, we study finite-pressure effects on ITG instabilities using the first global gyrokinetic particle-in-cell codes which work with full finite-pressure MHD equilibrium data. We note that microinstabilities in general equilibria were previously studied in the ballooning limit [6]. With respect to global ITG stability, we find that the dominant effect is related to the particle =B drift on the low-field side of the torus: The growth rates decrease with decreasing =B drift. In fact, the configurations are stable when =B is close to reversal.The ITG instability takes its free energy from the ion temperature gradient. It can be destabilized by the parallel motion (slab ITG), the poloidal magnetic drifts due to toroidicity (toroidal ITG), and the trapped-ion precession (trapped ion mode). The latter two destabilizing mechanisms are related to the magnetic drift,where B denotes the magnetic field, V the ion cyclotron frequency, y k and y Ќ the parallel and perpendicular particle velocities, and p the plasma pressure. From a waveparticle interaction diagnostic implemented in one of our codes, we find that particles with y Ќ ¿ y k contribute most to the instability. In a simple analysis which helps to understand the simulation results to be presented, the second term in Eq. (1) can therefore be neglected.For k k 0 and k c 0, the wave vector reduces to k nq=x 2 n=w, x being the straight-field-line poloidal angle [7], w the toroidal angle, n the toroidal mode number, and q the safety factor. In the local and fluid limits, the drift frequencies may then be defined asandwhere T i is t...

On finite β stabilization of the toroidal ion temperature gradient mode

“…Electrostatic approximation clearly breaks down when ␣ e approaches the critical value found in this study and in this respect the analysis in Ref. 7 is not self-consistent.…”

“…Recently, Fivaz et al 7 analyzed the ITG mode in electrostatic approximation with the effects of drift reversal in the magnetic drift frequency,…”

Attaining neoclassical transport in ignited tokamaks

“…Our numerical results corroborate their findings, and show that neglect of δB for A = 3 and A = 1.4 for these cases leads to an underestimate of the growth rate by factors of two to an order of magnitude or more. Analyses of advanced tokamak cases at both A = 1.4 and A = 3 have frequently neglected this effect [19], probably leading to a substantial underestimate of instability strength.…”

Parallel magnetic field perturbations in gyrokinetic simulations

“…Stabilization of microinstabilities via this mechanism has been proposed previously. 4 However, Berk and Dominguez 1 showed that this stabilizing effect is canceled by including compressional magnetic field fluctuations, which allow the plasma to carry its "self-dug" well. For this reason, the importance of retaining B ʈ in stability calculations at high ␤ has been commented on by other authors.…”